Abstract
On the Wasserstein space over a complete, separable, non-compact, locally compact length space, we consider the horo-functions associated to sequences of atomic measures. We show the existence of co-rays for any prescribed initial probability measure with respect to a sequence of atomic measures and show that co-rays are negative gradient curves in some sense. Some other fundamental results of this kind of functions are also obtained.
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Xiaojun Cui is supported by the National Natural Science Foundation of China (Grants 11631006, 11790272, 11571166). The project is funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD) and the Fundamental Research Funds for the Central Universities.
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Zhu, G., Wu, H. & Cui, X. Horo-functions associated to atom sequences on the Wasserstein space. Arch. Math. 115, 555–566 (2020). https://doi.org/10.1007/s00013-020-01490-z
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DOI: https://doi.org/10.1007/s00013-020-01490-z